Dropwise Condensation on Micro- and Nanostructured
Surfaces
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Citation
Enright, Ryan et al. "Dropwise Condensation on Micro- and
Nanostructured Sufaces." Nanoscale and Microscale
Thermophysical Engineering, Volume 18, Issue 3, July 2014.
pages 223-250.
As Published
http://dx.doi.org/10.1080/15567265.2013.862889
Publisher
Taylor & Francis
Version
Original manuscript
Accessed
Thu May 26 06:47:18 EDT 2016
Citable Link
http://hdl.handle.net/1721.1/85005
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publisher's site for terms of use.
Detailed Terms
Nanoscale and Microscale Thermophysical Engineering
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Dropwise Condensation on Micro- and Nanostructured
Surfaces
Manuscript Type:
Date Submitted by the Author:
Special Issue: Micro and Nano Structures for Phase Change Heat Transfer
24-Oct-2013
Enright, Ryan; Bell Labs Ireland, Alcatel-Lucent Ireland Ltd.,
Miljkovic, Nenad; Massachusetts Institute of Technology,
Alvarado, Jorge; Texas A&M University,
Kim, Kwang; University of Nevada, Las Vegas,
Rose, John; Queen Mary, University of London,
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Surface engineering, Condensation, Phase change
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Keywords:
UMTE-2013-1232.R1
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Complete List of Authors:
Nanoscale and Microscale Thermophysical Engineering
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Manuscript ID:
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Journal:
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Page 1 of 39
Dropwise Condensation on Micro- and Nanostructured
Surfaces
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Ryan Enright1,*, Nenad Miljkovic2,3, Jorge L. Alvarado4, Kwang Kim5 and John W. Rose6
1
Thermal Management Research Group, Efficient Energy Transfer (ηET) Department, Bell Labs Ireland,
Alcatel-Lucent Ireland Ltd., Blanchardstown Business & Technology Park, Snugborough Rd, Dublin 15,
Ireland
2
Department of Mechanical Engineering, Massachusetts Institute of Technology,
77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA
3
Department of Mechanical Science and Engineering, University of Illinois,
Urbana, Illinois 61822, USA
4
Department of Engineering Technology and Industrial Distribution and Department of Mechanical
Engineering, Texas A&M University,
College Station, Texas 77843, USA
5
Department of Engineering, University of Nevada, Las Vegas,
4505 Maryland Parkway, Las Vegas, Nevada 89154, USA
6
School of Engineering and Materials Science, Queen Mary, University of London,
London E1 4NS, UK
Abstract
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In this review we cover recent developments in the area of surface-enhanced dropwise condensation
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against the background of earlier work. The development of fabrication techniques to create surface
structures at the micro- and nanoscale using both bottom-up and top-down approaches has led to
increased study of complex interfacial phenomena. In the heat transfer community, researchers have been
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extensively exploring the use of advanced surface structuring techniques to enhance phase-change heat
transfer processes. In particular, the field of vapor-to-liquid condensation and especially that of water
condensation has experienced a renaissance due to the promise of further optimizing this process at the
micro- and nanoscale by exploiting advances in surface engineering developed over the last several
decades.
*
To whom correspondence should be addressed: ryan.enright@alcatel-lucent.com,
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Nanoscale and Microscale Thermophysical Engineering
Introduction
Understanding the mechanisms governing water condensation on surfaces is crucial to a wide
range of applications that have significant societal and environmental impact, such as energy conversion
[1–3], water harvesting [4,5], water desalination [6], thermal management systems [7–11] and
environmental control [12]. Water vapor preferentially condenses on solid surfaces rather than directly in
the vapor because of the reduced activation energy of heterogeneous nucleation in comparison to
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homogeneous nucleation [13]. While the excess energy of a surface controls the heterogeneous nucleation
process via the nucleation rate, it also determines the wetting behavior of the condensate, which has a
significant impact on the overall heat and mass transfer performance. Water vapor condensing on high or
low surface energy surfaces forms a liquid film or distinct droplets, respectively. The latter, termed
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dropwise condensation (DWC), is desired since it yields much higher heat transfer coefficients [14,15].
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However, high performance dropwise condensers have failed to find widespread application in industry
due to the difficulty in identifying a durable low-thermal-resistance DWC promoter for heat transfer
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materials with characteristically high surface energies [15,16].
The development of fabrication techniques to create surface structures at the micro- and
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nanoscale using both bottom-up (e.g., chemical oxidation, direct growth) and top-down (e.g., lithography
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with wet and dry etching) approaches has led to significant growth in the study of complex interfacial
phenomena. Advances in surface structuring and functionalization technologies for promoting DWC have
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allowed researchers to begin exploring the optimization of DWC at the micro- and nanoscales. In this
review we first summarize key theoretical and experimental developments in the area of DWC. Next, we
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detail several important surface functionalization approaches, highlighting some strengths and limitations.
We then discuss imaging techniques that are allowing insight into the condensation process at ever
decreasing length scales. Finally, we explore several enhanced condensation modes that rely on complex
surface modifications at the micro- and nanoscale. For a discussion on internal flow condensation in
microchannel geometries we refer the reader to a recent review [17].
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Classic dropwise condensation theory & experiment
The theory and mechanism of DWC on smooth surfaces have been well understood for around 50
years [15,18–21]. In a model proposed by Le Fevre and Rose an expression for the heat transfer through a
single droplet was combined with an effective mean droplet size distribution to determine the dependence
of surface heat flux on vapor-surface temperature difference ∆T [18,19]. Their single droplet heat transfer
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model considered the conduction resistance, the vapor-liquid interfacial mass transfer, the DWC promoter
layer resistance and the effect of interface curvature on the saturation temperature at the droplet surface;
which all play significant roles with the relative importance of each depending on droplet size. The
droplet surface curvature, along with condensate surface tension and surface subcooling (supersaturation)
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determines the size of the smallest thermodynamically-viable droplet and hence the number of activated
nucleation sites, while the interface mass transfer term is strongly dependent on pressure. The increase in
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site density causes the heat-transfer coefficient to increase with increasing vapor-surface temperature
difference while the increasing mass transfer resistance causes the heat-transfer coefficient to decrease
with decreasing pressure [15].
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Umur and Griffith provided an exact solution for the conduction resistance of a hemispherical
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droplet by incorporating the interfacial heat transfer coefficient directly into the analysis [22]. This
approach avoids the issue of infinite heat transfer at the edge of the droplets obtained by considering the
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interface and base of the droplet to be at two different temperatures. Also given was an approximation for
contact angles other than 90°. Later, Sadhal & Martin developed an expression for the combined
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conduction and interfacial resistance for arbitrary droplet contact angles between 0° and 90° [23]
validated by numerical simulation [24]. Other estimates have been provided for the case of droplets with
contact angles greater than 90° [25,26], but did not incorporate a heat transfer coefficient on the droplet
interface.
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Nanoscale and Microscale Thermophysical Engineering
Tanaka used population balance theory to evaluate the local droplet size by taking into account
the two mechanisms of growth: direct vapor accommodation onto the droplet and coalescence with
neighboring droplets to obtain predictions of the droplet size distribution for small non-coalescing
droplets [21]. Since that time, the population balance theory has been used to estimate the population of
droplets of a given size [27,28].
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Accurate DWC measurements need care to minimize non-condensing gas (NCG) content and
prevent build-up of a diffusion boundary layer [15,29,30]. NCG concentrations as little as 3 ppm
(µmol/mol) can result in significant error. NCG build-up near the surface as the vapor constituent of the
mixture is removed by condensation can result in significantly reduced vapor temperature at the
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condensing surface. In these circumstances the observed vapor-surface temperature difference is the sum
of the temperature drop in the gas-vapor diffusion boundary layer and the required temperature drop
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across the condensate. Error increases with condensation mass flux and is much more significant for
DWC where the condensation mass fluxes are larger and the temperature drop across the condensate is
much smaller.
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Accurate surface temperature and heat flux measurements are best achieved using flat plate
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geometries where heat flux and surface temperature can be accurately determined from slope and
intercept of temperature distributions in the condenser plate. This geometry is recommended for
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fundamental condensation measurements and results should be benchmarked against well-documented
data sets [30–36]. A set of repeatable data showing the dependence of heat flux on pressure and
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temperature and comparison with theory is given in Figure 1. It may be noted here that the theory is also
in fair agreement with data for ethylene glycol and mercury as well as predicting measurements of
dependence of heat-transfer coefficient on maximum droplet size [37]. A general correlation for steam
DWC, covering a range of pressures, is given by [15]:
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.
∆
∆
273.15
5
0.3
,
kW/m
K
K
K
kW/m2
Eq. 1
where q is the heat flux and T is the absolute temperature. Equation Eq. 1, which agrees closely with the
both experimental data and theory, is recommended as a benchmark for assessing the heat-transfer
performance of new promoting techniques on vertical flat plates.
For dropwise condensation on horizontal tubes Eq. 1 might be expected to underestimate the
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mean heat-transfer coefficient by not more than about 20% [29]. Where tubes have been used it is more
convenient to determine the heat flux from mass flow rate and temperatures rise of the coolant, which is
accurate to within 2% of temperature gradient measurements to determine heat flux [16,38,39].
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Furthermore, tube condensers are more prevalent in industry, making this geometry favorable for
practical benchmarking.
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Surface functionalization techniques
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In order to achieve DWC a functional coating that can impart a reduced surface energy is
typically required due to the high surface energy of typical heat transfer materials such as aluminum,
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copper, titanium and stainless steel. This is a particularly crucial area of DWC research since, in the ~80
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years since the discovery of DWC, a satisfactory solution has yet to found that simultaneously satisfies
durability, cost and performance requirements. Below we detail several major approaches to realizing
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suitably low excess surface energies, highlighting their primary strengths and limitations. A summary of
these approaches is given in
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Table 1.
Self-assembled monolayers
Self-assembled monolayers (SAMs) rely on the spontaneous formation of a thin molecular film (~1 nm)
on the condensing surface comprising individual molecules with hydrophobic tails pointing outwards
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Nanoscale and Microscale Thermophysical Engineering
from the surface that interacts with the condensate and a ligand that attaches to the condensing surface.
This functionalization approach has the advantage that it does not introduce a significant thermal
resistance. However, durability remains a primary concern. In early works, SAMs were applied, for
example, by immersing copper in a 1% solution of carbon tetrachloride for a period of typically 1 h
before rinsing with distilled water. Under laboratory conditions this coating technique gives ideal DWC
for some tens of hours before the coating is progressively removed resulting in a steadily decreasing heat
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transfer coefficient over the course of days [29]. Since this time, a range of SAM molecule options have
become available including a number of thiol (sulfur-based ligand) and silane (silicon-based ligand)
species with either hydrogenated or fluorinated end groups (tail) that strongly chemisorb with
metals/metal oxides and are easy to deposit [41]. In the field of DWC, thiols have been studied more
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extensively [42,43]. However, the use of silane SAMs in connection with the study of DWC has been on
the rise [38,44–51].
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In comparison to the silanes, thiols are less stable. Thiols tend to oxidize over short time scales
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when exposed to the ambient conditions or UV radiation; reducing to disulfides and sulfonates that wash
away easily from the surface with polar solvents such as water [4]. Thiols are also less thermally stable
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than silanes [52]. So while thiols are of use for laboratory studies, they appear to be of limited practical
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use. On the other hand, silanes are more stable due to covalent bonding with the surface.[41] Furthermore,
a range of self-healing strategies have been developed in the recent literature based on fluorinated silane
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chemistries that could significantly increase the longevity of these coatings[53,54]. Interestingly, there
appears to be only limited data available for the longevity of silane-based SAMs during condensation
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[55].
Polymers
Various polymer coatings have been used to promote DWC including polytetrafluoroethylene (PTFE),
parylene and silicones [16,34,56–59]. However, polymer coatings have only proved durable when the
layer thickness is such as to effectively offset the advantage of DWC [16]. This limitation may potentially
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be overcome using new binder materials to form a stronger bond between the functional polymer and the
substrate. Plasma-enhanced vapor deposition of ultra-thin fluoropolymer coatings have been used for
fundamental studies of DWC condensation [60]. In addition, initiated chemical vapor deposition of the
fluoropolymer thin films is an attractive functionalization method due to high coating conformality and
potential robustness [55,61].
Noble metals
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It was initially believed that DWC occurred naturally on noble metals [62–64]. However, it was
subsequently shown that clean noble metals give film condensation of steam [65]. Thus, DWC may be
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observed on noble metals due to the presence of physisorbed surface contaminants [66]. Therefore, the
barrier for implementing this method of promoting DWC has mainly been limited by the need to
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replenish surface contaminants to maintain DWC behavior.
Ion implantation
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In the mid 1980’s Zhang et al.[67] and later Qi et al.[68] reported that sustained DWC can be achieved
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through ion implantation of metal surfaces. This early work [69,70] was followed by a series of papers by
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Leipertz, Froba, Rausch and co-workers which systematically characterized the wettability and durability
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of ion implanted metal surfaces [71–77]. Carbon, nitrogen, and oxygen ion implantation of copper,
aluminum, titanium, and steel surfaces was demonstrated to produce coatings which promoted sustained
DWC over periods of multiple months [74]. The mechanism of promotion of DWC involves the
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formation of nanoscale roughness and chemical heterogeneities produced by particulate precipitates
bonded to the metal surfaces [73]. Significant heat transfer improvement is observed on ion implanted
surfaces at low subcooling levels, however, the surfaces demonstrate decreasing heat transfer
performance when the subcooling level is increased significantly coinciding with the observation of large
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Nanoscale and Microscale Thermophysical Engineering
irregular droplets and areas undergoing film condensation [73]. Thus far, however, this technique has not
yet been utilized in industry primarily due to its high cost.
Rare earth oxides
Recently, Azimi et al. provided experimental evidence that rare earth oxides (REOs) are intrinsically
hydrophobic and promote DWC of steam [78]. This approach may be potentially advantageous given the
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toughness of these ceramics compared to SAMs and polymers. However, heat transfer results on these
surfaces are not available at this time.
Imaging techniques
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Although conventional methods such as optical microscopy are helpful to investigate droplet
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growth and coalescence [79–81], environmental electron microscopy allows features smaller than a few
micrometers to be resolved and includes the techniques of environmental SEM (ESEM) and
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environmental TEM (ETEM). Generally, ESEM and ETEM have a limited operating pressure range (up
to 2.7 kPa) and thus have only been used to image condensation of water near its triple point (273.16 K
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and 611.73 Pa). The use of ESEM, which allows for imaging of specimens that are "wet," uncoated, or
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both by allowing gases in the specimen chamber, has been of particular interest for condensation research
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[82–84]. Figure 2a shows a schematic representation of this imaging technique whereby adjusting the
pressure of the water vapor in the specimen chamber and the temperature of the cooling stage, water
droplets condense and secondary electrons (SE) are collected to create a high resolution image of the
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process. Typically, images of droplets (Figure 2b) show strong topographic contrast such that dynamic
droplet growth can be observed [44,45,85–89], reliable contact angle measurements can be made and
individual droplet heat transfer rates can be calculated [85,90].
During ESEM imaging in the sub-10 µm regime, electron beam heating becomes important [91].
In situ ESEM condensation imaging avoiding substrate-related issues can be achieved by removing and
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transferring of a small part of the macroscale substrate to a thermally insulated sample platform (Figure
2a) [92]. The perpendicular orientation of the sample with respect to the electron beam limits the
absorbed energy and enables simultaneous visualization using secondary (SE - ESEM) and transmitted
electrons (TE - STEM) [93]. Figure 2c shows a comparison of ESEM to STEM imaging using the
technique, showing higher resolution and smaller beam heating effects. This technique has been used to
study different stages of droplet growth on structured surfaces providing insight into the transition of
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condensing liquid from nano-films forming within the structures, to discrete droplets forming on top of
the structure [92].
While ESEM imaging has recently become one of the most utilized condensation imaging
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methods, other techniques exist which allow for direct imaging beneath condensing droplets to better
understand local wetting states. Rykaczewski et al. demonstrated a direct method for nano-to-microscale
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imaging of complex interfaces using cryostabilization [94], cryogenic focused ion beam (FIB) milling,
and SEM imaging (cryo-FIB/SEM) (Figure 2d) [95]. This approach has recently been used for imaging of
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water droplets and frost structures condensed on superhydrophobic (SHS) and lubricant-infused surfaces
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(LIS) (see schematic layout of the process in Figure 2d) [95,96]. This approach enables identification of
individual phases using energy x-ray dispersive spectroscopy (EDS) and also provides quantitative
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information about interfacial areas between different phases. Other imaging techniques which have been
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applied to DWC research include infrared imaging and liquid crystal thermography [97–99].
Advanced imaging methods used in combination with quantitative analysis have facilitated
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understanding of how structure geometry and nucleation density affect the emergent droplet morphology
and wetting state. Although these methods provide high spatial resolution (<10 µm), limitations in
temporal resolution still make these techniques difficult to use at high heat fluxes when droplet growth
dynamics are faster than the image capture speed. Since ESEM software only enables capturing images at
rates up to 10 fps, Rykaczewski et al. used a screen capture software to capture their results with
maximum rate of about 55 fps [100]. Thus, ESEM imaging with rates of several hundreds of frames per
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Nanoscale and Microscale Thermophysical Engineering
second are achievable and could be even further speed up by balancing obtaining proper contrast through
electron beam current and dwell time adjustment (for example 300 ns). The primary roadblock to
achieving high speed ESEM is not the hardware, but the ESEM software.
Surface-modified dropwise condensation modes
In this section several different approaches to modifying condensation surfaces are described. A summary
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of the different approaches is given in
Table 2.
Superhydrophobic surfaces
Surface-roughness-modified wetting
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The use of hydrophobic surfaces with surface roughness/structures smaller than the capillary
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length scale (Bond number much smaller than unity) has been proposed to enhance condensation heat
transfer [9,10,42,43,46,47,91,92,101–105]. Research has focused on using a combination of roughness
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and low surface energy materials/coatings to create superhydrophobic surfaces, where apparent contact
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angles exceed 150° and contact angle hysteresis approaches 0° [106,107], for DWC to enhance droplet
shedding [26,108–110]. Because wetting interactions can be tuned using structure geometry, these
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surfaces promise a means to manipulate condensation behavior to realize droplet morphologies ranging
from highly pinned, i.e., Wenzel state [111], to superhydrophobic, i.e., Cassie state [112], where droplets
can shed passively at microscopic length scales via droplet coalescence [42].
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Considering a surface with roughness, r, defined by the ratio of the total surface area to the
projected area, Wenzel showed when the fluid wets all of the rough area, the apparent contact angle is defined by [111]:
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cos " cos ,
Eq. 2
where is Young’s angle [113]. Cassie and Baxter considered the case where the droplet rests on the tips
of the roughness and showed that the apparent contact angle $
cos $
is defined by [112]:
% &cos 1' 1,
Eq. 3
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where φ is the ratio of the solid area contacting the droplet to the projected area. The Wenzel state is less
desired owing to the higher adhesion typically associated with this wetting state [107]. As a result, many
studies have focused on creating and understanding superhydrophobic surfaces to limit droplet adhesion
and increase water repellency [106,107,114–117].
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In the case of condensation, however, the nucleation of droplets can initiate within the surface
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roughness and is a non-equilibrium wetting process, such that Equations Eq. 2 and Eq. 3, where
equilibrium is assumed, may not apply. Previous studies have shown that, on structured superhydrophobic
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surfaces with well-controlled geometries (Figure 3a), highly adhered Wenzel droplets form during vapor
condensation that are distinct from the highly mobile Cassie droplets when deposited using a syringe
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[102,105,107,118]. In fact, three distinct droplet types are found to exist during condensation; Wenzel
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(W) (Figures 3a, b), partially wetting (PW) (Figures 3c, d), and Cassie or suspended (S) (Figures 3e, f)
droplets. The type of droplet realized is dependent on the surface roughness geometry, nucleation location
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and nucleation density. Knowledge of the emergent droplet type, contact angle behavior and adhesion
needs to be properly characterized and understood in order to tailor the micro/nanostructured surfaces for
enhanced heat transfer [38].
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Rykaczewski et al.[119] and Enright et al.[44] demonstrated the relation between droplet growth
mode and underlying nanostructure. Specifically, both works showed that confinement of the base area of
growing droplet is necessary for formation of high contact angle droplets. Enright et al. showed that the
morphology of isolated droplets interacting with the surface structures during growth is due to energy
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Nanoscale and Microscale Thermophysical Engineering
barriers encountered by the droplet growing within the structured surface (Figure 4a) [44]. As a droplet
nucleates within the structure and grows to fill the unit cell (volume between structures), it can either
grow above the structure forming a ‘balloon’ like PW droplet (Figure 4b), or laterally spread into the
structure forming a highly adhered W droplet (Figure 4c) [44,119]. While the droplet wetting state is
dictated by the intricate liquid/structure interaction dynamics, Enright et al. showed that it can be
conservatively approximated by comparing the energies of the non-equilibrium advancing Cassie and
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Wenzel states with a dimensionless energy ratio:
( ∗
cos $*
cos ee
1
.
rcos Eq. 4
Equation Eq. 4 implies that, when E* > 1 (" , 1/ cos ), W droplet morphologies are favored, while
when E* < 1 (" - 1/ cos ), PW Cassie droplets should emerge [44].
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Previous studies have indicated that there must be a surface-structure length-scale dependency,
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i.e., microstructures [47,101,105] versus nanostructures [10,42,43,103,120], suggesting that global
thermodynamic analysis, though often used to explain observed condensation behavior
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[47,101,102,105,119], provides an incomplete description of the dominant wetting state realized during
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condensation [106]. In addition to the energy criterion (Eq. 4), the nuclei of the droplets need to be
separated by 2-5x of the spacing between the structures (Figure 4d) (⟨L⟩/l > 2−5, where ⟨L⟩ is the average
On
spacing between droplets and l is the characteristic spacing of the surface structures). If droplets grow and
merge too close to each other (⟨L⟩/l < 2−5), the contact line pinning energy barrier associated with
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individual droplet growth (Eq. 4) is bypassed and flooding of the surface results forming undesired highly
adhered W droplets (Figure 4e) [44]. Accordingly, a regime map defining the parametric space with
experimentally measured ⟨L⟩/l ratios and calculated E* in Figure 4f determines the emergent droplet
morphology for a wide variety of structure length scales, geometries and nucleation densities. Given this
regime map, an important aspect of maintaining nominal DWC behavior becomes being able to define
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surface structure spacing, l, that is smaller than the separation distances between nucleation centers at a
given supersaturation.
Droplet jumping
A key phenomenon associated with condensation on superhydrophobic (low adhesion) surfaces is that
when two droplets coalesce, the merged droplet can spontaneously jump away from (normal to) the
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condensing surface. This phenomenon was first reported in the case of mercury DWC on rough steel
surfaces by Kollera and Grigull [121]. The self-propelled motion is powered by the surface energy
released upon droplet coalescence [42], and the out-of-plane direction results from the impingement of
the liquid bridge between the coalescing droplets on the superhydrophobic substrate [42,122]. The
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jumping motion has been applied to a variety of phase-change systems [108], including
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superhydrophobic surfaces that are anti-dew and/or anti-icing [44,49,123–125], enabling the possibility to
enhance DWC with nanostructured surfaces [38,43,46,104,126,127].
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The self-propelled jumping offers an alternative method for transporting condensate in phase-change
systems, independent of any external forces or internal porous wick structures [128]. The autonomous
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transport can be used to return the condensate in closed-loop systems, such as vapor chambers, in a
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manner that is fundamentally distinct from the gravity- or capillarity-driven transport [129]. Recently,
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Miljkovic et al. discovered that condensed droplets become charged during the jumping process which
opens up the possibility for the control of condensate removal using external electric fields [60]. This may
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be particularly important for situations where entraining vapor flows begin to dictate the trajectories of
jumping droplets resulting in impeded heat transfer [129,130].
Despite considerable interests in the coalescence-induced jumping phenomena, much remains to be
understood about the self-propelled jumping process, which is of great practical interest. For example, in
designing vapor chambers, the jumping velocity is critical for evaluating the distance the self-propelled
droplets can travel [108,129]; in designing superhydrophobic condensers, the threshold radius is crucial
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Nanoscale and Microscale Thermophysical Engineering
for determining the average size of the condensate droplets [38,42]. Existing models explaining the
threshold radius employ an energetic argument assuming a somewhat arbitrary form of viscous
dissipation [131–134]. Such models should be further validated with a first-principle model of the
complex droplet coalescence process [135]. Future modeling efforts should ideally take into account the
surface textures, which introduce additional complexities including moving contact lines, partially wetted
cavities, and contact angle hysteresis [136] and asymmetric coalescence [9,127]. These modeling efforts
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should ideally draw on experimental evidences from both high-resolution electron microscopy and highspeed optical imaging.
Hierarchical superhydrophobic surfaces
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Chen and co-workers were the first to report that surfaces with hierarchical nanoscale and microscale
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topology are superhydrophobic during condensation and promote spontaneous droplet motion [42,43].
Inspiration for such hierarchical architecture comes from nature, for example, the superhydrophobic
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surface of the lotus leaf [137–141]. Although the mechanism of the two-tier roughness is still not
completely understood, Boreyko et al. suggested that a mixed Wenzel-Cassie state is possible for the
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water condensate, where the nano-tier remains dry but the micro-tier is preferentially wetted [142,143].
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The role of microscale topology on coalescence dynamics during condensation on hierarchical surfaces
been studied theoretically by Liu et al. [132,144], Chen et al. [10], and Rykaczewski et al.[123].
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Rykaczewski et al.[123] investigated condensation occurring on hierarchical superhydrophobic surfaces
consisting of microscale truncated cones with varied dimensions and pitch covered by dense array of
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nanotrees [10,119,145]. They found that the majority of mobile coalescence events on their hierarchical
superhydrophobic surfaces involved the merging of multiple droplets. Their results highlighted the
importance of microscale features and provide motivation for further studies of condensation on
hierarchical superhydrophobic surfaces with varied microscale topology. In addition, the authors
identified that the surface architecture promoting departure of the highest number of microdroplets
consisted of microscale features spaced close enough to enable transition of larger droplets into the Cassie
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state yet, at the same time, provided sufficient spacing in-between features to allow for mobile
coalescence.
Heat transfer on superhydrophobic surfaces
Heat-transfer models for condensation on superhydrophobic surfaces have recently been
advanced, being extended from those on smooth DWC surfaces, that deal with the trade-off between
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droplet mobility (preferring suspended droplets) and thermal conductance (preferring impaled droplets)
[45,46,86,108,146,147]. Miljkovic et al.[46] and Lee et al.[147] extended the Kim model [26], which
introduced a conduction resistance term for droplet contact angles greater than 90°, to incorporate
geometric details of the structured surface beneath condensing droplets. Furthermore, Miljkovic et al.
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considered the emergent droplet wetting morphology, non-constant contact angle droplet growth and
updated the droplet size distribution theory to include both constant and non-constant contact angle
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droplets growing on surfaces experiencing coalescence-induced droplet jumping [46]. Recently, the
feasibility of superhydrophobic nanostructures to enhance DWC has been experimentally demonstrated
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[38]. Heat transfer enhancements of approximately 30% were achieved on a SAM-functionalized copper
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oxide-based nanostructured surface relative to a smooth SAM-functionalized surface when the surface
was operating in a jumping droplet regime (Figure 5) [38]. However, increasing supersaturation led to
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flooding of the surface and degraded heat transfer performance. While demonstrated on nanostructured
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surfaces, the advantage of introducing hierarchically structured surfaces for enhancing condensation heat
transfer (besides the condensation area increase that accompanies a hierarchical architecture) remains to
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be shown. Cheng et al. have presented preliminary heat transfer data on a hierarchically-structured
surface [126]. However, during heat transfer experiments their surface was flooded and no heat transfer
enhancement was observed. Further investigation is needed to understand the role hierarchical structures
may play in enhancing heat transfer rates and to develop strategies to prolong the onset of surface
flooding to higher supersaturations.
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Nanoscale and Microscale Thermophysical Engineering
Bi-philic surfaces
It is well known that nucleation on hydrophobic surfaces requires a higher degree of
supersaturation than is required when condensing on hydrophilic surfaces [13,148]. Thus, bi-philic
surfaces that contain a combination of hydrophilic and hydrophobic regions to reduce the energy barrier
for vapor condensation while promoting droplet shedding have been explored in an effort to improve
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DWC. Kumagai et al. were among the first to explore the effects of bi-philic surfaces on condensation
heat transfer performance [149]. By patterning their condensing surfaces with alternating stripes of
hydrophobic and hydrophilic regions with dimensions at or above the capillary length scale, they showed
that heat transfer performance was bounded between the limits of complete DWC and filmwise
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condensation. More recently, wetting characterization of hybrid surfaces with characteristic length scales
below the capillary length has been carried out to study the effects of using alternating hydrophobic and
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hydrophilic strips [150,151] and hydrophobic/hydrophilic dots on a hydrophilic/hydrophobic background
[152] on dynamic droplet contact angles. This understanding is crucial in elucidating the trade-offs
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between using high-energy condensation sites versus the need to minimize contact angle hysteresis to
promote efficient droplet shedding.
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Varanasi et al.[153] investigated the use of hydrophobic-hydrophilic patterning in combination
with structured roughness with the aim of spatially controlling heterogeneous nucleation while facilitating
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efficient droplet shedding. Using a simple bottom-up deposition process, Mishchenko et al.[154] have
shown that functionalized hydrophilic polymers and particles deposited on the tips of a range of
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superhydrophobic structures can induce precise spatial control over water condensation at the micrometer
scale. However, results to date indicate that using structured bi-philic surfaces for condensation purposes
results in a significant contact angle hysteresis effect due to the hydrophilic tips [155]. Indeed, while the
apparent advancing angle is independent of the hydrophilic tip wettability, for a fixed structure geometry,
increased hysteresis is expected as the local receding contact angle of the hydrophilic tip decreases [152].
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He et al.[156] developed a unique hierarchically structured superhydrophobic surface comprised
of pores with hydrophilic polymer coatings at the base of the pores. Their approach allowed for the
efficient condensation of water on the hydrophilic region and surface-tension-driven droplet jumping
[142]. They found a significant increase in condensate removal using a bi-philic surface chemistry versus
a uniformly hydrophobic surface chemistry. Anderson et al.[157] studied a unique bi-philic structured
surface where the relative placement of the hydrophilic and hydrophobic regions on the surface were
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reversed compared to previous studies [153,155,158] resulting in hemi-wicking droplets [159]. Their
approach relied on Laplace pressure instability to gather droplets independent of coalescence-induced
droplet growth mechanics.
Lubricant-infused surfaces
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ee
Lubricant-infused surfaces (LIS) consist of micro/nano structures that are functionalized with a
low surface energy coating that are subsequently infused with a low surface energy lubricant that is
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immiscible with the wetting liquid that results in exceptionally low contact angle hysteresis. One of the
earliest reports of this phenomenon was in the context of ideal electrowetting surfaces [160], with further
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description in terms of maximizing droplet mobility [159]. Recently, a range of LIS characteristics were
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demonstrated based on inspiration from Nepenthes pitcher plants [161]. Since then, detailed theoretical
descriptions of the phenomenon have been developed [162–164]. LIS are a particularly attractive
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engineered surface solution because of their omniphobic [161], self-cleaning [162], self-healing [161],
and anti-fouling [165] characteristics. Daniel et al.[166] demonstrated the promise of LIS to function
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under elevated temperature conditions where superhydrophobicity tends to fail due to decreasing surface
tension. Kim et al. studied the wetting behavior of LIS for micro-, nano- and hierchically-structured
surfaces [167]. They found that nanostructures alone resulted in the best behavior under high shear
conditions in terms of lubricant retention and maintaining low contact angle hysteresis. Anand et al.
proposed LIS as a viable surface engineering approach to enhance condensation heat transfer based on the
observation of water droplet mobility for sizes as small as 100 µm (Figure 6a & b) [168]. Later, Xiao et
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Nanoscale and Microscale Thermophysical Engineering
al.[11] extended the concept of condensation on LIS one step further by introducing a bi-philic functional
coating that could increase the nucleation density of droplets due to the reduced interfacial energy
between the condensing water and the lubricant; a concept termed “immersion condensation.” Combined
with the inherent low contact angle and contact angle hysteresis characteristic of LIS, they demonstrated a
marked enhancement of ~100% in condensation heat transfer performance versus classic DWC in the
presence of NCGs (Figure 6c-e).
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Conclusions & Future Outlook
The field of DWC has experienced a significant resurgence thanks to new imaging techniques
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allowing unprecedented access to the growth of droplets on substrates and the proliferation of fabrication
techniques that is allowing researchers to realize increasingly sophisticated engineered surfaces.
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However, as new knowledge is gained it is important that past lessons are also appreciated. Guidelines
developed over ~80 years for performing condensation heat transfer measurements should be closely
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followed including test section design that removes the influence of NCGs. The number of studies
demonstrating condensation phenomena on enhanced surfaces greatly exceeds the number of studies
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quantifying condensation heat transfer performance. This gap needs to close in order for different
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approaches to be validated. At the very least, high definition imaging experiments should be performed
with the aim to provide an expectation of performance before carrying out global heat transfer
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experiments on large area samples [46]. Long-term condensation studies are needed to validate the
durability of new surface structuring and functionalization approaches. Physical failure mechanisms
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should be identified under both laboratory and industrial conditions and accelerated testing methods
should be explored. We stress that maintaining long-term DWC remains the primary barrier to practical
implementation for industrial applications. Furthermore, the scalability of surface structuring and
functionalization approaches needs to be considered in the context of likely applications.
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In superhydrophobic condensation, improved understanding of the droplet jumping process for a
range of surface characteristics and condensation conditions is needed. In light of the flooding mechanism
that has so far limited enhanced heat transfer rates on superhydrophobic surfaces, strategies including
structure scale reduction and control of droplet nucleation density should be explored. From the studies
reviewed here, recommendations can be made regarding the feasibility and applicability of
superhydrophobic surfaces for enhanced condensation. If the condensation heat flux is relatively low
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(<8 W/cm2) the ideal superhydrophobic surface should meet the following 5 criteria if it is to be
comparable to or exceed the heat transfer performance of a smooth dropwise condensing surface having
low contact angle hysteresis: 1) the partially wetting droplet morphology should be favored, 2) the
structure length scale should be minimized (<2 µm), 3) the density of the structures should be high, 4) the
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thermal conductivity of the structure material should be as high as possible, and 5) the hydrophobic
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coating covering the structure should be highly conformal and ultra-thin (<40 nm) in order to minimize
parasitic thermal resistances. However, if the condensation conditions are such that heat fluxes exceed
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≈8 W/cm2, a smooth dropwise condensing surface with low contact angle hysteresis will have better
performance due to nucleation site saturation and flooding of the superhydrophobic surface. Note, the
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limit of 8 W/cm2 is the current state-of-the-art superhydrophobic performance. With further reduction of
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structure length scale (increased structure density), this heat transfer threshold for jumping/flooding
should increase and make superhydrophobic surfaces a more viable option for high heat flux applications.
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The implementation of bi-philic surface chemistries and roughness at sub-capillary length scales
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for condensing surfaces is a potentially promising route to enhance condensation rates. The ability to
tailor both droplet growth and departure behavior using a range of wetting heterogeneity and structures
opens up a large design space for condensing surfaces. However, systematic global heat transfer
measurements and detailed heat transfer models for these surfaces are still lacking. Thus, there remains a
significant need for studies to demonstrate the efficacy of bi-philic surfaces in condensation heat transfer
applications.
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Nanoscale and Microscale Thermophysical Engineering
While the potential for heat transfer enhancement on LIS has been demonstrated, systematic
studies along with further theory development will be required to find the optimum design for these
surfaces in the context of heat transfer. A key question regarding LIS is the long-term operability of these
surfaces and the impact of progressive lubricant drainage on condensation heat transfer performance.
While this issue has yet to be systematically addressed in the context of condensation heat transfer, the
results of Kim et al. suggest that nanostructured LIS, rather than microstructured or hierarchical LIS, may
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be the most promising in minimizing lubricant loss [167]. However, the impact of lost lubricant during
water droplet shedding remains to be assessed. Furthermore, passively improving condensation
performance in the presence of NCG remains an outstanding issue though LIS have shown promise in
addressing this issue [11]. However, the mechanism by which LIS improves the performance of DWC in
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the presence of NCG remains poorly understood.
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Finally, while much recent research has focused on the interaction of condensing water with
structured surfaces, condensation rate enhancement techniques at the nano- and microscale for low
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surface tension liquids remains an outstanding problem. In the case of structured, low-energy surfaces,
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realization of the mobile Cassie state becomes increasingly difficult to achieve as the wetting angle of the
condensate reduces. Clever surface designs that spatially-control condensation coupled with structures
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that can promote a meta-stable Cassie wetting state may offer a solution. However, such an approach will
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still be limited by the increased nucleation rates expected for low surface tension liquids [13,148]. Here
LIS may offer a more feasible solution by maintaining low contact angle hysteresis for droplets with
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characteristically small contact angles. Thus, heat transfer measurements for such systems should be
pursued.
Nomenclature
E*
Dimensionless energy ratio
-
hc
Heat transfer coefficient
W/(m2 K)
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q
Heat flux
W/m2
<L>
Mean separation distance between nucleation sites
m
l
Surface structure spacing
m
12
Mass flux
kg/(s m2)
r
Roughness factor
-
T
Temperature
K
γsv
Solid vapor interfacial energy
J/m2
γsl
Solid-liquid interfacial energy
J/m2
γlv
Liquid-vapor interfacial energy
J/m2
θ
Young contact angle
°
θa
Advancing contact angle
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Cassie apparent contact angle
Wenzel apparent contact angle
$
°
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Acknowledgements
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°
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The authors would like to thank Prof. Konrad Rykaczewski, Prof. Chuan-Hua Chen and Prof. Kripa
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Varanasi for valuable discussions. Bell Labs Ireland thanks the Industrial Development Agency (IDA)
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Ireland for their financial support. N.M. gratefully acknowledges funding support from the MIT S3TEC
Center, an Energy Frontier Research Center funded by the Department of Energy, Office of Science,
Basic Energy Sciences under Award # DE-FG02-09ER46577.
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Figure Captions
Figure 1. Classical condensation heat transfer experiments. (a) Data for dropwise condensation of steam
on a copper surface functionalized with dioctadcyl disulphide [32]. Heat flux and vapor-surface
temperature difference measurements are shown for various vapor pressures. Different symbols denote
data taken on different days. The solid lines are from the theory of Le Fevre and Rose [18]. (b & c)
Dropwise condensation of steam at atmospheric pressure on a vertical copper surface functionalized with
dioctadecyl disulphide [40]. Scale bars: 20 mm (b) Heat flux, q = 0.4 MW/m2; subcooling, ∆T = 2 K;
condensation mass flux, 42 0.18 kg/m2 s. (c) Heat flux, q = 1.4 MW/m2; subcooling, ∆T = 4 K;
condensation mass flux 42 0.62 kg/m2 s.
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Figure 2. Condensing droplet characterization techniques. (a) Schematic showing the imaging process of
water condensation on nanostructured particles using primary (PE), secondary (SE) and transmitted (TE)
electron detectors [92]. (b) Constant base droplet growth on a hydrophobic surface imaged using the
gaseous secondary electron detector (GSED) at a 90° angle [119]. (c) Series of ESEM images illustrating
micro- and nanoscale imaging of water condensation on CuO particles. Top images show GSED detector
images, bottom show STEM images [92]. (d) Step-by-step schematic of the cryogenic-focused ion beam
(FIB)/SEM method: (i) water condensation on precooled sample, (ii) rapid plunge freezing in liquid
nitrogen slush (LN2), (iii) vacuum transfer and in situ conductive metal deposition, and (iv) cryogenicFIB/SEM milling and imaging [95]. (e) 52° tilt cryogenic-FIB/SEM images of water condensed on a
superhydrophobic surface consisting of silicon nanowires coated with a hydrophobic promoter [95].
Adapted with permission from references [92,95] (Copyright 2013, American Chemical Society) and
[119] (Copyright 2012, Royal Society of Chemistry).
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Figure 3. Condensing droplet contact angle. Time-lapse schematics of (a) Wenzel (W), (b) partially
wetting (PW), and (c) suspended (S) droplet morphologies during growth on the structured surface
(schematics not to scale). Environmental scanning electron microscopy (ESEM) images of droplets with
the (d) W, (e) PW, and (f) S morphologies on a nanostructured surface (h = 6.1 µm, l = 2 µm, d = 300
nm). Reprinted with permission from references [146] (Copyright 2013, American Society of Mechanical
Engineers) and [46] (Copyright 2012, American Chemical Society) .
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Figure 4. Effect of structure length scale and nucleation density on emergent droplet morphology.
(a) Schematic of a droplet growing within the confines of the structures. The liquid can either expand
horizontally by filling up more volume between the nanostructures or by increasing its contact angle and
forming a droplet [ref. [119]]. Condensed droplet growth observed using ESEM on structured surfaces
with (b) Cassie droplets where l = 2 µm and (c) Wenzel droplets where l = 4 µm [ref. [44]]. Scale bar for
(b, c) is 60 µm. Condensation behavior on a microstructured surface (l = 4.5 µm, d = 2 µm, h = 5 µm, and
E* = 0.75 ± 0.04) is shown at a fixed location with a scaled coalescence length of (d) ⟨L⟩/l = 3.54 ± 2.43
(PW droplets) and (e) ⟨L⟩/l = 2.04 ± 0.6 (W droplets) [ref. [44]]. Scale bar for (d, e) is 50 µm. (f) Regime
map characterizing the dominant wetting behavior observed during condensation with coordinates of ⟨L⟩/l
and E*. Cassie morphologies (red □) emerge at large ⟨L⟩/l and E* ≲ 1 (shaded region). Wenzel
morphologies (blue ○) emerge at low ⟨L⟩/l and/or E* ≳ 1 [ref. [44]]. Adapted with permission from
references [44] (Copyright 2013, American Chemical Society) and [119] (Copyright 2012, Royal Society
of Chemistry).
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Figure 5. Experimental and predicted (Eq. 1) condensation heat transfer coefficients during dropwise, and
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jumping-droplet condensation on a tube sample (DOD = 6.35 mm, DID = 3.56 mm, L = 131 mm) for
saturated vapor pressures Pv of (a) 2.2 kPa, (b) 2.7 kPa, and (c) 3.3 kPa [38]. Error bars indicate the
propagation of error associated with the fluid inlet and outlet temperatures and pressure measurement.
The jumping surface error bars are the largest due to the relatively low heat fluxes measured (q < 80
kW/m2), corresponding to the smaller fluid inlet to outlet temperature difference. The model predictions
(lines) were obtained from Eq. 1 and are in good agreement with DWC on the tube.
Figure 6. (a) Concept of condensation on a LIS and (b) an ESEM image of water condensed on a LIS
[168]. Water condensation on (c) a dropwise condensing tube surface and (d) a copper-oxide-based LIS
tube surface. (e) The overall (vapor to cooling water) heat transfer coefficient for the LIS surface
undergoing immersion condensation in the presence of NCG (PNCG = 30 Pa) is compared to the smooth
dropwise (c) and flooded superhydrophobic surfaces [11]. Approximately 100% increase in performance
is observed for the LIS surface versus the dropwise condensing surface. Note the generally low overall
heat transfer coefficients due to the presence of NCGs. Adapted with permission from references [168]
(Copyright 2013, American Chemical Society) and [11] (Copyright 2012, Nature Publishing Group).
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Table 1. Summary of surface functionalization techniques for DWC.
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Table 2. Summary of surface modified condensation modes for DWC.
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Figure 1
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Figure 2
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Figure 6
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Nanoscale and Microscale Thermophysical Engineering
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Table 1
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Table 2
157x117mm (300 x 300 DPI)
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